# Modeling

# Overview

Our modeling is includes 2 parts

##### - Simulation the cleaning rate of Biofilm with specific concentration engineered bacteria

##### - Calculate the amount of bacteria recovered by magnetic force

# Background and Aim

The simulation is carried out in an aquarium of L1×L2×L3. The model assumed that the biofilm is fully covered on the inner wall of the aquarium and is not affected by external conditions. It can be regarded as a macroscopic condition, and then the inner wall of the aquarium is divided into each of the unit cubes may grow with different thickness of biofilm. Once the engineering bacteria enter the cube, it can be regarded as under microscopic conditions. When the engineering bacteria enter the water, because the engineering bacteria do not have flagella in this experiment, they cannot move autonomously. The moving speed of the engineering bacteria under macro conditions is the water flow speed by default.

# Symbol Description

# Model assumptions

1.The biofilm fully covers the inner wall of the aquarium.

2. When engineering bacteria enter the aquarium, they will move randomly at a speed equal to the flow speed.

3. The size of an engineered bacteria is a unit point

4. Once the engineered bacteria come into contact with the biofilm, there will be two situations.If it adheres to the surface of the biofilm, the engineered bacteria will initiate a reaction to remove a single point of the biofilm. If it does not adhere to the surface, it will bounce in the original direction. Go back to a unit point and continue to move randomly. The probability of occurrence of the first case is p, the probability of occurrence of the second case is (1-p)

5. Once within the time T, the engineered bacteria have not cleared the plaque, the engineered bacteria will be regarded as dead by default.

6. The biofilm clearance rate reaches 95%, and the default is that the biofilm has been completely removed

7. Under the macro background, the moving speed of engineering bacteria defaults to the water flow speed in the aquarium.

# Cellular automata and netlogo

Different from the general dynamic model, cellular automata is not determined by strictly defined physical equations or functions, but is composed of a series of model construction rules.

The construction of cellular automata does not have a fixed mathematical formula, it has a complicated structure, many variants, and complex behavior. Therefore, its classification is also difficult. Since the birth of cellular automata, the study of cellular automata classification is an important research topic and core theory of cellular automata. Based on different starting points, there are many classifications for cellular automata. Among them, the most influential is the dynamic behavior-based cellular automata classification made by S. Wolfram in the early 1980s, and the dimension-based cellular automata classification is also the simplest and most commonly used The division. In addition, in 1990, Howard A. Gutowitz proposed a hierarchical and parameterized classification system based on the Markov probability measurement of cellular automata behavior (Gutowitz, H. A., 1990).

In our project, given that the fish tank is a complex system due to the influence of water flow, cellular automata is used to solve the problem, and netlogo software is used to solve the problem.

Netlogo is a programmable modeling environment used to simulate natural and social phenomena. It was initiated by UriWilensy in 1999 and is continuously developed by the Center for Linked Learning and Computer Modeling (CCL). Its research and development purpose is to provide a powerful and easy-to-use computer-aided tool for scientific research and educational institutions.

NetLogo is a programming development platform that inherits the Logo language, but it has improved the Logo language can only control a single individual. It can control thousands of individuals in modeling. Therefore, NetLogo modeling can be very good. Simulate the behavior of micro-individuals and the emergence of macro-models and the relationship between them. NetLogo is a programming language and modeling platform used to simulate natural and social phenomena. It is especially suitable for simulating complex systems that develop over time.

Based on it we developed a simulation program about our programe

# Model I and Model II

*Model I：*

Affected by covid-19, our experiment did not obtain data, so we built a sub-model to obtain some data needed in the simulation

This model is based on the cell principle and the law of motion in the water (the specific rules will be explained in Model II). We have established a 2D bacterial membrane random collision model in a 1cm*1cm*1cm square, and we Acquired data: When placing n engineered bacteria in a square of one centimeter, there is a probability of P to remove the bacterial film

Model I process

*Model II：*

Under macroscopic conditions, the biofilm is cleaned in unit cubes. Whenever the number of engineering bacteria entering a unit cube reaches a certain value, the biofilm in the cube will be removed with a certain probability given by model 1. In an aquarium, the velocity of engineering bacterial equals to the flow velocity of water.

According to above principle, netlogo is used to stimulate this process. Here is the software:

Figure 2.1: control desk

Figure 2.2 initial situation

In figure 2.2, blue balls stand for engineering bacteria. The grey surface strands for the inner wall of aquarium which is fully covered by biofilm. The engineering bacteria will move according to flow velocity of water.

Figure 2.3 situation after 0.068h

In Figure 2.3, the red surface stands for cleaned biofilm. With such stimulation process, the biofilm clearance rate is calculated when the concentration of bacteria is 48000 num/mL

Figure 2.5 Biofilm situation

To increase clearance rate, the initial concentration will be increased.

Figure 2.6 Final biofilm situation

In this model with the data from wetlab, it is proof that the engineering bacteria can clear the biofilm efficiently.

Figure 2.7 final biofilm situation

The logic grapth of the model I and II

# Model III

On the basis of the previous model, we have established a simulation recovery model for the recovery problem, modified on the basis of the previous simulation of the water flow field, and established a magnetic field simulation model.

As shown in the figure below, the arrows represent the engineering bacteria, the entire cuboid represents the recycling pipeline, and the red part is the magnet. When the bacteria move in the pipe at the speed of V (unit velocity), they will be affected by the magnetic force F (unit magnetic force). If the bacteria successfully reach the end of the pipeline (green area), conclude that they are escape

Figure 3.1

Figure 3.2

And got the relationship between the bacterial concentration and the recovery rate.

Through many simulations, it can be seen that our design has strong cleaning ability and will not damage the biological membrane used in the aquarium.

# Code for our model

https://github.com/jack10124/UM_Macau

# Reference

* Melanie Mitchell. ”Complexity: A Guided Tour ”ISBN 9787535767134 *